01.01.05 (Probability theory and mathematical statistics)
Birth date:
25.12.1952
E-mail:
,
Keywords:
mathematical statistics; inverse problems; asymptotic methods of statistics; nonparametric hypothesis testing; large deviations; sequential estimation; sufficient statistics.
Subject:
The asymptotic structure of nonregular statistical experiments was investigated. The structure of minimal sufficient statistics was studied in multivariate case and in the case of discontinuous densities. The asymptotically minimax estimators have been found in deconvolution problems. The relation of rates of convergence in minimax and Bayes settings has been investigated. The optimality of rates of convergence of Tikhonov regularizing algorithm has been shown in stochastic setting. The necessary and sufficient conditions of distinguishability of sets of hypothesis and alternatives in $L_2$ was obtained. The asymptotically minimax tests were obtained in the problem of testing hypothesis in $L_2$ if the sets of alternatives are ellipsoid in $L_2$ with the balls in $L_2$ deleted. The asymptotic minimaxity of tests of Kolmogorov, omega-squared and chi-squared types was proved under natural nonparametric sets of alternatives. The lower bounds for probabilities of large deviations of tests and estimators were proved under assumptions that almost can not be improved.
Biography
Graduated from Faculty of Mathematics and Mechanics of Leningrad State University (LSU) in 1976 (department of theory of probability and mathematical statistics). Ph.D. thesis was defended in 1979. D.Sci. thesis was defended in 1992. A list of my works contains more than 40 titles.
Main publications:
Ermakov M. S. On distinguishability of two nonparametric sets of hypothesis // Statist. Probab. Lett., 2000, v. 48, p. 275–282.
Ermakov M. S. Minimax estimation in a deconvolution problem // J. of Phys. Ser. A Math. Gen., 1992, v. 25, p. 1273–1282.
M. S. Ermakov, D. Yu. Kapatsa, “On uniform consistency of Neyman's type nonparametric tests”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10:2 (2023), 212–225; Vestn. St. Petersbg. Univ., Math., 10:2 (2023), 212–225
2.
M. S. Ermakov, “On uniform consistency of nonparametric tests”, Zap. Nauchn. Sem. POMI, 526 (2023), 78–89
3.
M. S. Ermakov, “Local asymptotic normality of likelihood ratio in moderate deviation zone”, Zap. Nauchn. Sem. POMI, 525 (2023), 71–85
2022
4.
M. S. Ermakov, “Nonparametric signal detection with small values of type I and type II error probabilities”, Zap. Nauchn. Sem. POMI, 510 (2022), 124–142
2021
5.
M. S. Ermakov, “Chi-squared test for testing of homogeneity”, Zap. Nauchn. Sem. POMI, 501 (2021), 160–180
2020
6.
M. S. Ermakov, “On uniform consistency of nonparametric tests. II”, Zap. Nauchn. Sem. POMI, 495 (2020), 147–176
M. S. Ermakov, “On moderate deviation probabilities of empirical probability measures for contiguous probability measures”, Zap. Nauchn. Sem. POMI, 454 (2016), 112–120; J. Math. Sci. (N. Y.), 229:6 (2018), 671–677
2015
11.
M. S. Ermakov, “On conistent hypothesis testing”, Zap. Nauchn. Sem. POMI, 442 (2015), 48–74; J. Math. Sci. (N. Y.), 225:5 (2017), 751–769
M. S. Ermakov, “Asymptotically efficient importance sampling for the bootstrap”, Zap. Nauchn. Sem. POMI, 431 (2014), 82–96; J. Math. Sci. (N. Y.), 214:4 (2016), 474–483
M. S. Ermakov, “On asymptotically efficient statistical inference on a signal parameter”, Zap. Nauchn. Sem. POMI, 420 (2013), 70–87; J. Math. Sci. (N. Y.), 206:2 (2015), 159–170
14.
M. S. Ermakov, “Large Deviation Principle for moderate deviation probabilities of empirical bootstrap measure”, Zap. Nauchn. Sem. POMI, 412 (2013), 138–180; J. Math. Sci. (N. Y.), 204:1 (2015), 90–115
S. V. Bulyarskii, L. N. Vostretsova, M. S. Ermakov, “Determination of energy parameters of electronic states in semiconductor carbon nanotubes”, University proceedings. Volga region. Physical and mathematical sciences, 2012, no. 4, 205–213
2008
16.
M. S. Ermakov, “Nonparametric Hypothesis Testing with Small Type I or Type II Error Probabilities”, Probl. Peredachi Inf., 44:2 (2008), 54–74; Problems Inform. Transmission, 44:2 (2008), 119–137
M. S. Ermakov, “On semiparametric inference in moderate deviation zone”, Zap. Nauchn. Sem. POMI, 351 (2007), 129–140; J. Math. Sci. (N. Y.), 152:6 (2008), 869–874
M. S. Ermakov, “Importance sampling for simulation of large and moderate deviation probabilities of tests and estimators”, Teor. Veroyatnost. i Primenen., 51:2 (2006), 319–332; Theory Probab. Appl., 51:2 (2007), 279–290
M. S. Ermakov, “Minimax detection of signal in weighted Gaussian white noise”, Zap. Nauchn. Sem. POMI, 320 (2004), 54–68; J. Math. Sci. (N. Y.), 137:1 (2006), 4516–4524
M. S. Ermakov, “On asymptotically efficient statistical inference for moderate
deviation probabilities”, Teor. Veroyatnost. i Primenen., 48:4 (2003), 676–700; Theory Probab. Appl., 48:4 (2004), 622–641
M. S. Ermakov, “On large deviations of type II error probabilities of Kolmogorov and omega-squared tests”, Zap. Nauchn. Sem. POMI, 298 (2003), 80–110; J. Math. Sci. (N. Y.), 128:1 (2005), 2538–2555
2001
22.
M. S. Ermakov, “Probabilities of large deviations in Banach spaces”, Zap. Nauchn. Sem. POMI, 278 (2001), 86–111; J. Math. Sci. (N. Y.), 118:6 (2003), 5555–5569
M. S. Ermakov, “On the Lower Bound of the Exact Asymptotics for the Large-Deviation Probabilities of Statistical Estimates”, Probl. Peredachi Inf., 35:3 (1999), 54–66; Problems Inform. Transmission, 35:3 (1999), 236–247
M. S. Ermakov, “On Bayes sequential estimation of location parameter of unsmooth density”, Zap. Nauchn. Sem. POMI, 260 (1999), 130–154; J. Math. Sci. (New York), 109:6 (2002), 2122–2140
1997
25.
M. S. Ermakov, “Asymptotic minimaxity of chi-square tests”, Teor. Veroyatnost. i Primenen., 42:4 (1997), 668–695; Theory Probab. Appl., 42:4 (1998), 589–610
M. S. Ermakov, “Asymptotic minimaxity of tests of the Kolmogorov and omega-square types”, Teor. Veroyatnost. i Primenen., 40:1 (1995), 54–67; Theory Probab. Appl., 40:1 (1995), 41–51
M. S. Ermakov, “Minimax nonparametric testing of hypotheses on the distribution density”, Teor. Veroyatnost. i Primenen., 39:3 (1994), 488–512; Theory Probab. Appl., 39:3 (1994), 396–416
M. S. Ermakov, “On lower bounds of probabilities of moderate and Cramér type large deviations of tests and estimators”, Zap. Nauchn. Sem. POMI, 216 (1994), 52–61; J. Math. Sci. (New York), 88:1 (1998), 36–42
M. S. Ermakov, “Large deviations for empirical probability measures and statistical tests”, Zap. Nauchn. Sem. POMI, 207 (1993), 37–59; J. Math. Sci., 81:1 (1996), 2379–2393
M. S. Ermakov, “Minimax detection of a signal in Gaussian white noise”, Teor. Veroyatnost. i Primenen., 35:4 (1990), 704–715; Theory Probab. Appl., 35:4 (1990), 667–679
M. S. Ermakov, “Minimax Estimation of the Solution of ill-Posed Convolution Type Problem”, Probl. Peredachi Inf., 25:3 (1989), 28–39; Problems Inform. Transmission, 25:3 (1989), 191–200
M. S. Ermakov, “Asymptotically Efficient Sequential Estimation of the Location Parameter of Non-Smooth Densities”, Teor. Veroyatnost. i Primenen., 34:3 (1989), 479–490; Theory Probab. Appl., 34:3 (1989), 430–440
1988
35.
M. S. Ermakov, “On Asymptotically Optimal Equivariant Sequential Estimation of Location Parameter for a Smooth Density”, Teor. Veroyatnost. i Primenen., 33:2 (1988), 323–335; Theory Probab. Appl., 33:2 (1988), 304–315
M. S. Ermakov, “Asymptotically minimax criteria for testing non-parametric hypotheses on the probability density”, Zap. Nauchn. Sem. LOMI, 166 (1988), 44–53
1984
37.
M. S. Ermakov, “On sufficient statistics for families of distribution with variable support”, Zap. Nauchn. Sem. LOMI, 136 (1984), 27–47
1981
38.
M. S. Ermakov, “On the rank of necessary and sufficient statistics for a sample of multivariate distributions”, Zap. Nauchn. Sem. LOMI, 108 (1981), 57–71; J. Soviet Math., 25:3 (1984), 1146–1154
1980
39.
M. S. Ermakov, “About properties of some random processes arising in the theory of statistical estimation”, Zap. Nauchn. Sem. LOMI, 98 (1980), 48–60; J. Soviet Math., 21:1 (1983), 31–39
40.
M. S. Ermakov, “On a sufficient statistics for families of distributions with variable support of density. I”, Zap. Nauchn. Sem. LOMI, 97 (1980), 62–82; J. Soviet Math., 24:5 (1984), 521–536
M. S. Ermakov, “Asymptotic behavior of statistical estimates of parameters for multidimensional discontinuities density”, Zap. Nauchn. Sem. LOMI, 74 (1977), 83–107; J. Soviet Math., 34:1 (1986), 1413–1427
S. V. Bulyarskii, M. S. Ermakov, “The effect of gamma-ray irradiation on the properties of GaAs-based p-n junctions”, University proceedings. Volga region. Physical and mathematical sciences, 2009, no. 3, 133–137
Contact us: